Connectionist teaching

I recently read the study by Askew et el (1997) called Effective teachers of numeracy in primary schools: teachers beliefs practices and pupils learning and it introduced me to a term called connectionist teaching. Connectionist teachers have "beliefs based around both valuing pupils methods and teaching strategies with an emphasis on establishing connections within mathematics." The study compared this style of teaching with discovery teaching and transmission teaching. It found that teachers with a strong connectionist orientation are more likely to have classes that made greater gains than those classes of teachers with strong discovery or transmission orientations.

So what do connectionist teachers do?

According to the study, connectionist teachers lessons are generally characterised by a high degree of focused discussion. These discussions were carefully monitored to bring out key strategies and ideas on the concept being taught. Pupils were expected to be able to explain their thinking process rather than just giving an answer to a question.

Connectionist teachers make "connections within mathematics." For example showing how expanding brackets in algebra has similarities to multiplying integers, rather than trying to link to real life contexts. I believe the most effective way of making those connections is through showing multiple representations. By using a consistent representation for multiple topics, students are able to notice similar methods and strategies. Below are a few examples from twitter of using representations to show a concept.

Visually solving equations using algebra counters and a vector model. @MEJ0778

Gattegno charts showing the effect of multiplying by 10, 2 and then linking to indices within algebra. @MrACrampton

Making use of bar modelling on mathsbot.com to find a fraction of an amount. Could also link to sharing in a ratio.

I don't think we should overwhelm students with 5 or 6 representations for the same thing however if we carefully choose them we can use it to enhance understanding and make connections between topics.

Connectionist teaching is not a complete contrast to discovery or transmission but embodies the best of both of them in its acknowledgment of the role of both the teacher and the pupils in lessons. I like to think of it as being teacher directed as opposed to teacher led or pupil led.

Equivalent Fractions with Ratio Tables

The following is a slide taken from NCETM Checkpoints. I was happy with the fraction pair on the right but the left stumped me! Then I had that 'aha' moment! What I used to do I never used to teach equivalent fractions like the one on the left to my classes. I would just use arrows to multiply both numerator and denominator to find an equivalent fraction, very similar to the fractions on the right. The issue with this though is, like me, students don't necessarily see all of the multiplicative relationships between the fractions as well as within the fraction. They are missing that key knowledge to support them answering the first pair of fractions. What I do now Ratio tables allow students to see those multiplicative links. By doing this it makes questions like the checkpoints task much easier for students to do. Disclaimer: this isn't the only way I teach equivalent fractions. I also show students how prime factors can also help us. There will be a future...

Literacy in Maths

I'm a Maths teacher, I teach numbers. Why is Literacy so important for me? Well….here's why: "Literacy is fundamental for success in school and later life. Students who cannot read, write and communicate effectively are highly unlikely to access the challenging academic curriculum in secondary school and are more likely to have poor educational outcomes across all subjects." (Link 3) Unfortunately there are a lot of Maths teachers who believe (wrongly) that literacy is a thing that the English department do. They see it as a tick box for observations. Rather than being an essential component of students being able to learn maths. - So what does it look like in Maths? Answer the question: Blindle 4x + 6 Are you able to do it? This is the challenge a lot of students face in Mathematics. Subject specific vocabulary can seem really confusing to a lot of students. Understanding what a keyword is asking of students is often the hardest part of a question and can hold s...

Percentages with Ratio Tables

What if I said you could teach your students one thing and they could answer everything to do with Percentages? Don't believe me? Let me show you: Finding a percentage of an amount Q: Find 20% of 925 Increasing/Decreasing by a percentage Q: Decrease 45 by 16% Expressing as a percentage Q: A cereal bar weighs 24g. The cereal bar contains 3.6g of protein. Work out what percentage of the cereal bar is protein Percentage Change Q: Rebecca bought a dress for £80. She later sold it for £116. Find the percentage profit. Reverse Percentages Q: A car increases in value by 35% to £2500. What was its original price? Ratio tables can be used for it all. There is obviously going to need to be some further teaching about what an increase/decrease is, how to work out the multiplier etc, but it is a great tool we should all be using more often You may have worked out by now that I like using Ratio tables.

Cameron Setter

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